Short answer: Josephson parametric amplifiers boost weak microwave signals with very little added noise, which is what superconducting qubit readout needs. A 2014 Nature Communications paper used a Josephson parametric phase-locked oscillator for single-shot, non-destructive qubit readout with Rabi oscillation contrast above 90%, and a 2015 Science paper reports a traveling-wave amplifier with 75% quantum efficiency that can read out 20 qubits. These are laboratory results reported by the authors.
Why readout needs near-quantum-limited amplifiers
Detecting single-photon-level signals is particularly challenging at low microwave frequencies, as the 2015 abstract points out. Readout of a superconducting qubit produces such a weak signal, so amplifier noise matters directly for how fast and how reliably the qubit state can be read.
2014: a phase-locked oscillator
The Nature Communications abstract explains that the parametric phase-locked oscillator was originally a logic element for digital computers more than 50 years ago, based on a nonlinear element such as a ferrite ring. The authors realize one with Josephson-junction circuitry and operate it as a sensitive phase detector. They demonstrate demodulation of a weak binary phase-shift keying microwave signal of the order of a femtowatt. Applied to dispersive readout of a superconducting qubit, they report high-fidelity, single-shot and non-destructive readout with Rabi oscillation contrast exceeding 90%.
2015: a traveling-wave amplifier
The Science abstract introduces a superconducting amplifier based on a Josephson junction transmission line. Unlike standing-wave parametric amplifiers, the authors say this traveling-wave design achieves high gain over a bandwidth of several gigahertz with enough dynamic range to read out 20 superconducting qubits. They introduce a subwavelength resonant phase-matching technique to do this. Benchmarking with weak measurements, they report a quantum efficiency of 75%, or 70% including noise added by amplifiers that follow. They say its compact lumped-element design gives it broad applicability to microwave metrology and quantum optics.
2018: pump depletion
A 2018 Physical Review B paper is titled "Quantum-limited parametric amplification with Josephson circuits in the regime of pump depletion". Only the title was readable when this post was written, so its results are not described.
What the two designs have in common
Both the 2014 and 2015 papers use Josephson-junction circuitry to provide amplification at microwave frequencies, and both tie the result to superconducting qubit readout. They differ in the amplifier itself: the 2014 device is a phase-locked oscillator used as a phase detector, while the 2015 device is a transmission line built to give gain over a wide band. The abstracts report different measures, contrast in one case and quantum efficiency in the other, so the numbers cannot be compared directly.
Limits
These are device papers from 2014 and 2015, and the figures are the authors' own measurements on their setups. A quantum efficiency of 75% is below the ideal limit, and the abstracts do not compare amplifier designs head to head, so no ranking is implied.
FAQ
Why do qubits need special amplifiers?
The readout signal is at the single-photon level, which is hard to detect at low microwave energies.
What did the 2014 paper achieve?
Single-shot, non-destructive readout with Rabi oscillation contrast above 90%.
What is special about the traveling-wave design?
High gain over several gigahertz of bandwidth and enough dynamic range to read out 20 qubits, per the 2015 abstract.
How efficient was it?
A quantum efficiency of 75%, or 70% including following amplifiers, per the authors.
Is this commercial hardware?
The abstracts describe laboratory devices only.
All field notes